Question

You are on the west bank of a river that is flowing north with a speed of 1.2 m/s. Your swimming speed relative to the water is 1.5 m/s, and the river is 60 m wide. What is your path relative to the earth that allows you to cross the river in the shortest time? Explain your reasoning.

Answer 1

head straight across the river (perpendicular to the bank).

Step-by-step explanation:

To cross the river in the shortest time first your velocity should be relative to the earth has to have the largest possible component to the bank

suppose,

S be the swimmer

E be the earth

W be the water

`u_(x/y)` be the velocity of X relative to Y

resultant velocity relative to E will be:

`u_(S/E)=u_(S/W)+u_(W/E)`

`u_(W/E)` is parallel to the bank so,

`u_(S/E)` has its largest component perpendicular to the bank when
`u_(S/W)` is in that direction

so to cross the river in the shortest time you should straight across the current will then carry you downstream so your path relative to the earth is directed at angle downstream